Progressive tightening devices causing the relative displacement of two elements are already known. In these devices, one of the elements can be considered as fixed and the other as movable, the object being to vary progressively the tension of the movable element, and thereby the tightening force. A device of this type is disclosed, e.g., in U.S. Pat. No. 2,205,742, and comprises a pinion permanently engaged, by diametrically opposite teeth, with the teeth of two parallel racks which are driven in opposite directions upon rotation of the control pinion. Such a device has the disadvantage of a relatively complex structure, and, in view of its reversability, does not provide absolute assurance of safety. In other words, it is necessary to supplement it with a locking device in order to maintain the pinion firmly in a position corresponding to a given tension adjustment, if untimely disadjustment is to be avoided.